Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
When a shape is cut into parts that each cover the same amount of space, each part is a unit fraction of the whole. Split a rectangle into 6 equal-area parts and each part is 1/6 of the rectangle's area. This standard brings geometry and fractions together, building on second-grade work with halves, thirds and fourths.
A key insight is that equal parts do not have to look alike. A square can be cut into fourths as four small squares, as four thin strips or as four triangles from the corners to the center. In each case the parts have the same area, so each is 1/4 of the square. Students should be able to partition shapes in more than one way, explain why the parts are equal (for instance by counting grid squares or by cutting and rearranging), and reject partitions where the parts look similar but have different areas. This careful thinking about equal area strengthens the meaning of the denominator in 3.NF.A.1.
Students may reject triangles and rectangles as fourths of the same square. Cut and rearrange them to show they cover the same area.
A circle cut into 4 unequal pieces is called fourths. Remind students that equal area is required before naming a fraction.
Some write 6 instead of 1/6 for the area of each part. Ask what part of the whole one piece is.
Freehand partitions of circles often produce unequal pieces. Use folding or grid paper to create accurate equal parts.
A square on grid paper covers 16 small squares. Show two different ways to split it into 4 parts with equal area and name each part.
Answer: Each part is 1/4 of the square's area, even though the strips and the small squares look different.
Give students paper squares and rectangles to fold and cut into equal parts in as many ways as they can find, then share and check by overlaying or counting grid squares. Displaying several different "fourths" of the same square side by side sparks rich discussion.
Assessment items show partitioned shapes and ask which shows thirds or which part is 1/6, or ask students to draw lines to partition a shape. Distractors often include unequal parts.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) 1/6
Each of 6 equal-area parts is one sixth of the whole, written 1/6.
Answer: A) 1/4
There are 4 parts with equal area, so each is 1/4 of the square.
Answer: B) A square cut into 3 pieces of different sizes
Thirds must have equal area. Three pieces of different sizes are not thirds.
Answer: 3
24 ÷ 8 = 3 grid squares in each part. Each part is 1/8 of the shape.
Answer: D) Yes, the two triangles have equal area
Cutting corner to corner gives two identical triangles with equal area, so each is 1/2.
Answer: 1/8
One of 8 equal parts is 1/8.
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
A full lesson with slides, activities and an exit ticket on partitioning shapes into equal areas, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.G.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn partitioning shapes into equal areas into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. They must have equal area. Different-looking parts are fine as long as each covers the same amount of the whole.
Each equal-area part is described as a unit fraction of the whole, such as 1/4, which directly supports the meaning of fractions in 3.NF.A.1.